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Foil 31 CPS713 Case Study II) Computational Features of Numerical Relativity

From Master set for Overview of Case Studies of Computational Science CPSP713 Master for Overview -- Autumn Semester 1994. by Geoffrey C. Fox * Critical Information in IMAGE
The theory is very nonlinear:
  • For instance one of the elliptic constraints can be written:
  • CFD is also nonlinear as have terms such as
Boundary Conditions at Infinity are those of computational electromagnetics (CEM)
  • Not those familiar from CFD
  • One needs to look for wave solutions and these waves are precisely what LIGO experiment will detect
  • Curiously I see that methods used in CEM such as method of moments are not being used in Numerical Relativity
    • NR solves evolution equations and identifies oscillatory wave solution
    • Waves very sensitive to numerics -- small numerical errors can be amplified as wave propagates
    • Numerical approximation can introduce an effective dissipative term which has small coefficient but enhanced by large propagation distance

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